Jointly segmenting a collection of images with shared classes is expected to yield better results than single-image based methods, due to the use of the shared statistical information across different images. This paper proposes a Bayesian approach for tackling this problem. As a first contribution, the proposed method relies on a new prior distribution for the class labels, which combines a hierarchical Dirichlet process (HDP) with a Potts model. The latter classically favors a spatial dependency, whereas the HDP is a Bayesian nonparametric model that allows the number of classes to be inferred automatically. The HDP also explicitly induces a sharing of classes between the images. The resulting posterior distribution of the labels is not analytically tractable and can be explored using a standard Gibbs sampler. However, such a sampling strategy is known to have poor mixing properties for high-dimensional data. To alleviate this issue, the second contribution reported in this paper consists of an adapted generalized Swendsen-Wang algorithm which is a sampling technique that improves the exploration of the posterior distribution. Finally, since the inferred segmentation depends on the values of the hyperparameters, the third contribution aims at adjusting them while sampling the posterior label distribution by resorting to an original combination of two sequential Monte Carlo samplers. The proposed methods are validated on both simulated and natural images from databases.